A.C. Fundamentals - Phasor Diagram at Series Resonance
1 Answer
At series resonance, a circuit containing a resistor (R), inductor (L), and capacitor (C) is excited by an AC voltage source at a frequency that causes the reactance of the inductor and capacitor to cancel each other out. This results in a purely resistive impedance and maximum current flow through the circuit. In a series resonance circuit, the phasor diagram helps visualize the relationships between the various voltages and currents.
Here's how the phasor diagram looks at series resonance:
Voltage Across the Resistor (VR):
The voltage across the resistor (VR) is in phase with the current (I). This is because the resistor's impedance is purely resistive, and there is no phase shift between voltage and current.
Voltage Across the Inductor (VL):
The voltage across the inductor (VL) leads the current (I) by 90 degrees. This is because the inductor's impedance is purely reactive, and the current lags behind the voltage by 90 degrees.
Voltage Across the Capacitor (VC):
The voltage across the capacitor (VC) lags the current (I) by 90 degrees. This is also because the capacitor's impedance is purely reactive, and the voltage lags behind the current by 90 degrees.
In a phasor diagram for series resonance:
The total voltage (VT) of the AC source is the vector sum of the voltages across the resistor (VR), inductor (VL), and capacitor (VC).
The total current (I) is the same throughout the circuit and is in phase with the voltage across the resistor.
At resonance, the magnitudes of the inductive and capacitive reactances are equal, and their effects cancel out. This means that the voltage across the inductor and capacitor are equal in magnitude and opposite in phase, resulting in their cancellation.
The phasor diagram at series resonance helps illustrate these relationships visually. It's important to note that the exact positions and angles of the phasors in the diagram depend on the specific values of resistance, inductance, and capacitance in the circuit, as well as the frequency of the AC source.
Remember that a series resonance circuit is characterized by a minimum impedance and maximum current at the resonant frequency, making it an important concept in AC circuit analysis and design.
Here's how the phasor diagram looks at series resonance:
Voltage Across the Resistor (VR):
The voltage across the resistor (VR) is in phase with the current (I). This is because the resistor's impedance is purely resistive, and there is no phase shift between voltage and current.
Voltage Across the Inductor (VL):
The voltage across the inductor (VL) leads the current (I) by 90 degrees. This is because the inductor's impedance is purely reactive, and the current lags behind the voltage by 90 degrees.
Voltage Across the Capacitor (VC):
The voltage across the capacitor (VC) lags the current (I) by 90 degrees. This is also because the capacitor's impedance is purely reactive, and the voltage lags behind the current by 90 degrees.
In a phasor diagram for series resonance:
The total voltage (VT) of the AC source is the vector sum of the voltages across the resistor (VR), inductor (VL), and capacitor (VC).
The total current (I) is the same throughout the circuit and is in phase with the voltage across the resistor.
At resonance, the magnitudes of the inductive and capacitive reactances are equal, and their effects cancel out. This means that the voltage across the inductor and capacitor are equal in magnitude and opposite in phase, resulting in their cancellation.
The phasor diagram at series resonance helps illustrate these relationships visually. It's important to note that the exact positions and angles of the phasors in the diagram depend on the specific values of resistance, inductance, and capacitance in the circuit, as well as the frequency of the AC source.
Remember that a series resonance circuit is characterized by a minimum impedance and maximum current at the resonant frequency, making it an important concept in AC circuit analysis and design.